Direct semi-parametric estimation of the state price density implied in option prices

TL;DR

This paper introduces a semi-parametric method for directly estimating the implied state price density from option prices without assuming a specific underlying asset model, ensuring no-arbitrage consistency.

Contribution

It proposes a novel semi-parametric approach modeling the log of the SPD as a smooth function, improving estimation accuracy and flexibility over parametric models.

Findings

Method performs well in simulations

Accurate estimation of SPD from real data

Ensures no-arbitrage conditions

Abstract

We present a model for direct semi-parametric estimation of the State Price Density (SPD) implied in quoted option prices. We treat the observed prices as expected values of possible pay-offs at maturity, weighted by the unknown probability density function. We model the logarithm of the latter as a smooth function while matching the expected values of the potential pay-offs with the observed prices. This leads to a special case of the penalized composite link model. Our estimates do not rely on any parametric assumption on the underlying asset price dynamics and are consistent with no-arbitrage conditions. The model shows excellent performance in simulations and in application to real data.